I suggest you to find a roommate, and split the fee.
I rented various apps over the last years in NY. From $750 a week (near lafayette avenue) up to $5,000 a month in the Chelsea area. But in the end, it wasnt worth staying in any of those places. Its fun to be in New York, but at the end i felt much safer and "at ease" in Miami. Although im not living there anymore either.
You have to make sure you really are suited to live in a big city. If you didnt grow up there, its hard to adjust and acclimate to the way of living. And with a budget of $1500 i wouldnt recommend it. Why not find a nice quite place in a state where you pay $1200-1400 for a home, instead of renting a small app in a bad "hood".
Maybe check out this site:
http://www.roommateclick.com/new-yor...ate/listings/h